ECON20001

Intermediate macro

Assignment #1

Due Monday September 9th 2pm AEST

Style. requirements [1 point]: This assignment requires the submission of a spreadsheet or a simple script. Please keep THREE decimal places in your answers and include your spreadsheet or script. as an appendix. You can use Excel, Google Sheets, Matlab, Python etc. in your calculations. Please take care in presenting your work and answers clearly.

Question 1 — Extended IS-LM Model [8 points]

In this question, your task is to review the IS-LM model developed in the lectures. You will then extend it with some novel behavioral assumptions that you have not yet seen, and compare the efficacy of policy under the different assumptions.

Suppose a closed economy (Economy A) with standard assumptions, including:

C(Y, T) = c0 + c1(Y − T)

I(Y, i) = b0 + b1Y − b2i

Md = $Y × L(i)

where 0 < c0, c1, b0, b1, b2 and c1 + b1 < 1. Treat fiscal variables, G and T as exogenous, and assume that the central bank runs an active monetary policy, adjusting Ms so that i = ¯i.

(a) Derive the IS and LM relations for Economy A. (1 point)

During lectures, students raised the idea that household savings would directly respond to the interest rate. We will model this by updating the consumption function:

C ′ (Y, T, i) = c0 + c1(Y − T) − c2i

where c2 > 0.

Figure 1: Credit Spread on Corporate Bonds

Although firms use household savings for investment, typically this is achieved through some third-party financial intermediary, like a bank. Usually, the bank charges a firm an interest rate that is higher than the interest rate paid to households. The amount charged will depend on the risk of the investment, where the firm pays a higher rate for riskier investments.

The difference between the interest rate on a risky asset and a safe asset is known as the risk premium or credit spread. For example, Figure 1 shows the premium that risky private firms pay over the rate on safe government bonds. Note that the premium for riskier BBB-rated firms is higher than that of the relatively safer A-rated firms. In addition, note that the risk premium appears to spike during high-risk/low-growth episodes; this is most clear in relation to the period just after the GFC (2008-2009).

We will model the above by updating the investment function:

I ′ (Y, i + p(Y )) = b0 + b1Y − b2(i + p(Y ))

where p(Y ) is a risk premium that is decreasing in Y . Assume the following premium function:

p(Y ) = p0 − p1Y > 0

where 0 < c2, p0, p1. Call this extended model Economy B.

(b) Derive the IS and LM relations for Economy B. (1 point)

(c) What upper bound(s) should be put on p1 (if any)? Why? (1 point)

For each of parts (d) and (e), assume that common parameters and exogenous variables are the same in each economy (e.g. both have the same c0, c1, . . .); they only differ by the new parameters introduced in Economy B. Provide explanations using mathematics, suitable graphs, and economic intuition.

(d) In which economy would expansionary fiscal policy be more effective? (2 points)

(e) In which economy would expansionary monetary policy be more effective? (Hint: you may need to consider the efficacy under different values for c2 and p1). (3 points)

Note, question 1 does not provide you with any numbers for the parameters and exogenous variables. Although you can use numbers to get a sense of how this model works, your final submission should apply generally (i.e., the only restrictions on the parameters/variables are those provided or otherwise justified by economic reasoning).

Question 2 — Dynamic AS-AD model [16 points]

Since the COVID-19 crisis, demand for Australian goods and services has boomed. Your task is to understand how this aggregate demand shock affects the Australian economy and the use of monetary policy in stabilising the economy. You will use the Dynamic Aggregate Supply-Aggregate Demand model (developed in Lecture 10, 11 and 12) to analyze this scenario.

For simplicity, suppose the natural level of output is constant. Each period lasts a year. Interest rate and inflation are expressed in percentage points. The parameter values of the model are given in Table 1 below.

Table 1: DAS-DAD model – Benchmark Parameter Values (η is used in part (e) only)

(a) Using the parameter values in Table 1, calculate the long-run equilibrium values of inflation, output and the nominal and real interest rates. (1 point)

(b) Suppose the economy was initially in its long run equilibrium. At year t = 1 the economy was hit by a persistent aggregate demand shock ε > 0 that lasts for two years and then reverts to zero. In particular, the aggregate demand shock takes the value εt = 1 for two years (t = 1, 2) before reverting to zero at t = 3. Starting in the long-run equilibrium, use the parameter values in Table 1 to calculate the magnitudes of the impact effects at t = 1 on inflation, output, nominal and real interest rates. Explain how to can recover the values of inflation, output, nominal and real interest rates from t = 2 onwards. (3 points)

(c) Use a spreadsheet program to calculate and plot the time-paths of inflation, output, real and nominal interest rates for 25 years (t = 0, 1, . . . , 25). Describe the inflation, output, real and nominal interest rates dynamics associated with this aggregate demand shock. Explain how monetary policy responds to these inflation and output gaps. (3 points).

(d) Suppose the RBA decides to respond more aggressively to the output gap by setting θπ = 0.3 and θY = 1.5. Keeping all other parameters as in Table 1, recompute the time paths of output, inflation, nominal and real interest rates for 25 years after the initial demand shock (t = 0, 1, . . . , 25). Explain how the policy change affects the time paths of inflation, output, nominal and real interest rates. Is there a policy trade-off between inflation and output? Explain. (3 points)

(e) Suppose instead of an active central bank using the standard monetary policy rule (MPR), the nominal interest rate is determined by the following monetary market rate determination (MMR) against a fixed money supply:

it = ρ + ηEt [πt+1] + η(Yt − Y¯),                           (MMR)

where η > 0 is the sensitivity of money demand to changes in the nominal interest rate. Note that with fixed money supply, a long-run equilibrium would imply an inflation rate of zero, πt−1 = πt = 0. All other assumptions are the same as the benchmark model.

(i) Derive the new DAD and DAS equations. (2 points)

(ii) Suppose the economy was initially in its long run equilibrium. At year t = 1 the economy was hit by a persistent aggregate demand shock ε > 0 that lasts for two years and then reverts to zero. In particular, the aggregate demand shock takes the value εt = 1 for two years (t = 1, 2) before reverting to zero at t = 3 (i.e., it is the same shock from above). Compute the time paths of output, inflation, nominal and real interest rates for 9 years after the initial demand shock (t = 0, 1, . . . , 9). Describe the results and give economic intuition for them. (3 points)

(iii) Choose one assumption of the model. Critically reflect on its contribution to the results in part (e)(ii), how reasonable you think the assumption is, and why. (1 point)